[1.bl (5 points) Suppose a steelworks is considering whether to purchase from Mi

Question

[1.bl (5 points) Suppose a steelworks is considering whether to purchase from Mine A or Mine B. They intend to purchase from Mine B, which offers a lower rate per ton of coal, unless it can be shown that coal from Mine B has on average, lower heat-producing capacity than coal from Mine A. The analysis has been performed in JMP and is provided here (with some values omitted). Assume all conditions necessary are satisfied, then: t Test Mine B-Mine A Assuming unequal variances Difference 140.00 t Ratio Std Err Dif Upper CL Dif 23.08 Prob >It 0.0829 Lower CL Dif 303.08 Prob>t 0.9585 Confidence (i) State the appropriate hypotheses (ii) Calculate the test statistic. (ili) Determine whether or not to reject the null hypothesis using = 0.05. 70.50 DF 7.858758 Hint: Be careful with the order of the subtrac- tion, it is stated on the JMP output 0.95 Prob

Explanation / Answer

let X denotes the heat producing capacity of coal from mine B

Y denotes the same of coal from mine A.

assumtion is that X~N(u1,sigma12)   and Y~N(u2,sigma2) where sigma1 and sigma2 are not equal.

we want to test whether coal from mine B has lower heat producing capacity or not

that is whether u1 is less than u2 or not

i) hence the appropriate hypothesis are

H0: u1-u2=0    vs alternative hypothesis H1: u1-u2<0   [answer]

ii) the value of test statistic is

T=(Xbar-Ybar)/standard error(Xbar-Ybar) which under H0 follows a t distribution

given from the JMP output Xbar-Ybar=-140 standard error(Xbar-Ybar)=70.50

hence the value of the test statistic is t=-140/70.50=-1.9858 [answer]

iii) since the alternative hypothesis is left tailed hence the p value is

p=P[T<-1.9858] where T follows a t distribution with df=7.858758 [from JMP output]

now from the output it is given that P[T<t]=0.415

hence p=0.0415

level of significance is given as alpha=0.05

hence p<alpha

hence null hypothesis is rejected [answer]

1.c) hence based on the sample data at ahnd at 5% level of significance H0 is rejected and it is concluded that coal from mine B has lower heat producing capacity.

hence the steelwork should purchase from mine A as mine B has lower heat producing capacity [answer]

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